For these opacity curves,
the logarithmic average opacity slope \(p_{\textnormal {UV}}=\Delta \log \kappa /\Delta \log \lambda \) 
between H \(\beta \)  (\(\lambda _{\mathrm {H}\,\beta }=486\)  nm) and H \(\alpha \)  is
roughly \(p_{\textnormal {UV}}\approx -0.5\)  to \(-1\) .
Larger dust grain size distribution powerlaw exponent values \(q\)  and smaller values of \(a_{\rm min}\)  make the slope steeper, that is, \(p_{\textnormal {UV}}\)  more negative,
while
\(a_{\rm max}\)  essentially does not change the slope much (see Figure 3 of [1]}) and only decreases the absolute amount of extinction.
For comparison,
the extinction law of [2]}, valid at H \(\alpha \)  and H \(\beta \) , has
\(p_{\textnormal {UV}}=-1.2\)  (\(p_{\textnormal {UV}}=-0.9\) ) for \(R_V=3.1\)  (\(R_V=5\) ).
[3]} recently adjusted the [2]} extinction law with \(R_V=3.1\)  and obtained \(p_{\textnormal {UV}}=-1.4\) .
We note that the fundamental reason why our curves are flatter than the empirical ISM curve is not yet understood.
